Question

What is the inverse equation of `y=4x-3`?

Answer 1

`f^{-1}:y=(x+3)/4`

Explanation:

When finding the inverse of a function it helps to think of the function in terms of x and y.

`f:y=4x-3`

where f is a function stating that y is equal to the right hand side.

Then you switch the x's and y's and write it as the inverse function for x.
`f^{-1}:x=4y-3`

However, to get the inverse function for y, we must rearrange the equation to get y on the left hand side along with `f^{-1}:` so that we get the expression `f^{-1}:y=`some value.

`f^{-1}:x=4y-3`

`f^{-1}:x+3=4y` //add 3 to both sides

`f^{-1}:(x+3)/4=y` //divide both sides by 4

Therefore, the inverse function is `f^{-1}:y=(x+3)/4`